§2.Chaos, order and orderly. Misconceptions about Chaos Theory

Ever wondered why chaos is needed and how to avoid it? Chaos is destruction, suffering, order is stability, security, prosperity. But order is not always good and chaos is bad. In Hitler's Germany, order, as it was understood there, brought prosperity to Germany and suffering to other nations. And in modern society those in power try to build such an order so that only they feel good, but such a imbalance sooner or later ends in an explosion, as protest sentiments grow on the part of those who are dissatisfied with this “order” and want a fair distribution of wealth and rights. In the history of states, there are always wars, devastation, chaos and times of relative stability. After cataclysms, a person strives to restore order, because only in conditions of stability, security, predictability, and confidence in the future, does he feel comfortable. But then, despite the apparent stability and security, chaos inevitably arises. Entire civilizations burned in its furnace. Why and how to avoid differences between “good and bad”? We feel these changes every day. Ups always end in downs. Why, how to prevent this?.. Only the mind, which needs to be developed, can level out these differences. And differences between “good and bad” arise due to the instability of the psyche that fear creates. The alternation of the activity of the two halves of the brain is inherent in man (and in every living creature) by nature. This is necessary for a two-sided, objective assessment of reality, in order to comprehend it, otherwise you simply cannot survive. The greater the pressure on the psyche of fear, the stronger the difference between “good and bad.” Fear interferes with the stability of the psyche, and in order to cope with it, we wedge ourselves on different “correctities”, thereby giving our thinking a one-sided direction, which is accompanied by a breakdown to the opposite extreme. Any extreme sooner or later leads to a dead end, from which CHAOS forcibly helps to break out. It sweeps away all the established correctness that has failed and led to a dead end, destroys all logical structures in order to develop and build new approaches to the created dead end situation, and begin to build from scratch new order , corresponding to the changed conditions. That is, under these conditions, chaos brings renewal, although the process itself is very painful. Perseverance in wrongness, which was previously considered correct, but under changed conditions has ceased to be so, can lead to death. Breaking habitual connections is always painful... If chaos is allowed to grow and become uncontrollable, it can lead to a catastrophe of planetary proportions. The slide towards disaster is prevented by fear, which forces one to reconsider previous approaches to solving problems, but often this happens belatedly, when a person is already on the brink of death. Reason forces us to act proactively, but, unfortunately, in people it is still poorly developed and consumption at any cost comes first. Society has not yet matured to rational behavior and fear and chaos that follows unreasonable behavior will force it to rationality... What is the essence of reason, since it will still be based on the differences between “good and bad”, on the alternation of the activity of opposites, on which life itself is based? And there will always be a bias towards “I want”, that is, consumption, without which a person cannot survive. The essence of reason is to level out these differences, to reduce the amplitude of oscillations between opposites, then there will be no “first I did it, and then I thought or didn’t think at all,” but there will be a review of the final result from “I want” and making a reasonable decision that will allow the desire satisfy, and not harm yourself. The mind strictly limits the ambitions of the EGO if they are harmful to the whole. Will this suppression of desires not result in harm to the animal instincts on which life is based, because “I want” is primary? How to grasp this fine line and what role does chaos play in all this? The mind does not suppress instincts; on the contrary, it gives them complete freedom. By allowing, they limit themselves, but through understanding the situation. Reason makes consciousness clear and emotions completely liberated. What contributes to their emancipation? The emotional chaos that the brain strives for. But this is not a random throwing of emotions, but a transfer of them into a state of “emotional broth”, from which they are extracted from the situation. Remember a time when you found yourself in dead-end situations from which there was no way out. Fear stuck you in the habitual, promoted as “correctness” and you could not break out of this vicious circle. You were plagued by depression until chaos completely destroyed all the “correct” structures that had been built and forced you to start thinking about the situation in a new way from a “clean slate”. That is, it was the transfer of thoughts into a state of chaos, in which there is no logic, that allowed you to reconsider your attitude towards the situation that had failed and develop new approaches to solving the “unsolvable problem.” It happens that fear gets so stuck on the problem that depression becomes the “norm of life” and then life becomes not a joy. In this case, you need to try to let go of the problem, “don’t give a damn” about it, let your thoughts float freely and get a good night’s sleep. During deep sleep, the brain itself will return to a state of correctness, through the collapse of all incorrectly built emotional connections and transferring them to a state of emotional broth. At the same time, we must stop clinging to the old, which has failed, and subject it to harsh criticism. You need to shake yourself properly and wake up from your depressive hibernation... Translating emotions into a state of “emotional broth” makes thinking flexible, not conservative, capable of perceiving the world directly, without self-deception, and using all feelings to comprehend reality, without dividing them into “bad” and “good.” The state of “emotional soup” can be called “intelligent chaos.” The more stable your attention, the stronger your energy power, the smaller the amplitude of oscillations between opposites, the more undistorted the feelings, the more reasonable and correct the decisions made, the less likely it is to fall into chaos, since there is no one-sided direction of thinking, which means there is no accumulation of irritations, with a breakdown to the opposite extreme. It's like being on a tightrope with a pole over an abyss. The more stable the balance (the smaller the differences between balancing), the further, wider and deeper you see, because the fear of falling into the abyss weighs less on you and you can relax to a greater extent. As soon as there is a threat of falling down, fear arises, which creates chaos, which, in turn, forces you to destroy the incorrectly built connections that led to the emergence dangerous situation and adjust your actions taking into account all factors, that is, use intuition... Sustained attention is beneficial to a person in all respects. It is the mind that guides a person along the divine path of development. It also prevents the accumulation of irritations and the emergence of chaos. The mind allows you to flexibly adapt to constantly changing conditions and constantly renew yourself, without resorting to the surgical intervention of chaos. 07/21/2016

Chaos (Lorentz attractor)

Order and chaos... Two extremes observed in the real world. Clear, obedient a certain order changing events in the space and time surrounding us - the movement of planets, the rotation of the Earth, the appearance of Halley's Comet on the horizon, the measured beat of a pendulum, trains running on schedule. And, on the other hand, the chaotic throwing of a ball in a roulette wheel, the Brownian motion of a particle under random impacts of “neighbors,” random vortices of turbulence formed when a fluid flows at a sufficiently high speed.

Until recently, any branch of technology, any production was characterized by the desire to organize the operation of all apparatus and devices in a stable static mode. Order, balance, stability have always been considered almost the main technical advantages. How can one not be afraid of external disorder, uncertainty, instability, inevitable energy losses - these obligatory companions of disequilibrium? Perhaps the bravest people in technology were the builders who managed to overcome this psychological barrier and began to incorporate an element of uncertainty into the designs of towers, high-rise buildings, and bridges—the ability to oscillate. Disordered processes can also lead to disasters. For example, if the profile of the wings or tail of aircraft is chosen incorrectly, a terrible phenomenon can occur in flight - flutter - a combination of torsional and bending disordered vibrations. When a certain flight speed is reached, flutter leads to the destruction of the entire structure - at one time this phenomenon turned out to be perhaps the most serious obstacle to the development of jet aviation. Subsequently, Academician M.V. Keldysh developed the theory of unstable oscillations and methods to combat them, and only his work made it possible to cope with flutter by slowing down - damping - oscillations. Thanks to this damping, aircraft structures became stable even in difficult unsteady conditions characteristic of aerodynamics. It is interesting that one of Keldysh’s monographs, published in 1945, is called “Shimmy of the front wheel of a three-wheeled chassis.” Shimmy is an American version of the foxtrot, according to the laws of which the wheel “dances.” Shimming the wheels of aircraft landing gear during takeoffs and landings also led to self-exciting irregular oscillations and, ultimately, to the destruction of aircraft. Based on Keldysh's theory, this defect was eliminated. So basic science once again demonstrated its practical usefulness.

In real nature, many chaotic processes take place, but we do not perceive them as chaos, and the observed world seems quite stable to us. Our consciousness, as a rule, integrates and generalizes information perceived by the senses, and therefore we do not see small “jitters” - fluctuations - in the nature around us. The plane rests reliably in air turbulent vortices, and although they pulsate randomly, the lifting force of the plane can be calculated with an accuracy of several kilograms as a certain average value. From deep space, signals from satellites and space objects come to Earth, and from a gigantic sea of ​​chaotic interference it is possible to “catch” the necessary information. Actually, all radiophysics is based on the “sorting out” of useful data and harmful “noise” according to certain statistical patterns.

How are ordered and chaotic phenomena related to each other and how to formulate (in a meaningful and mathematically rigorous way) rules that would describe the continuous transition from strict orderly patterns to random chaos, and vice versa?

A classic example of such dual behavior of the same object, a single physical system, is the flow of a liquid (see Fig. 1):

Rice. 1

This is how turbulence occurs. The cylinder is surrounded by a fluid flow, for example, moves in it. Flow is conveniently characterized by the “Reynolds number” Re, which is proportional to the flow velocity and the radius of the cylinder. At low Reynolds numbers, the fluid flows smoothly around the body in it, and then, as the flow speed increases, vortices are formed in the fluid. The higher the speed of the incoming flow (the higher the Reynolds number), the more vortices are formed and the more complex and intricate the trajectories of fluid particles become. When turbulence develops, the flow velocity behind the body pulsates in an unpredictable manner.

By observing a moving flow of water in conditions where we can regulate its speed, for example, in the bed of a dam or when moving a glider, we can perceive a gradual transition from a stable smooth - laminar - flow to an uneven, pulsating, vortex - turbulent. At low speeds, the liquid flows steadily and smoothly, as they say, stationary. When the flow speed increases, vortices begin to form in the flow, but even at this stage the picture still remains stationary. As the speed increases, the vortices are increasingly entrained by the flow, and an unsteady flow arises. The water suddenly swirls in whirlpools and generally behaves as if, on its own whim, it rushes here and there. Large vortices give rise to an unpredictable, disordered state, and, finally, the flow structure becomes completely turbulent - chaotic.

How to explain such a strong difference between laminar and turbulent flows, what is the mystery here? Unfortunately, despite the ongoing efforts of a large number of researchers from different countries, no one has yet managed to either describe a stormy, disordered (this is the translation of the Latin word turbulentus) turbulent flow, or find analytically, that is, using formulas, the conditions for the transition to it from laminar (Latin lamina means “plate”, “strip”).

But then a natural question arises: why is it so difficult to describe the chaotic turbulent behavior of a fluid mathematically? The fact is that some physical systems (in fact, most of them) turn out to be very “sensitive” - they react violently even to weak influences. Such systems are called nonlinear, since their response is disproportionate to the strength of the “disturbing” influence, and is often completely unpredictable. For example, if you slightly push a stone lying on the top of a cliff, it will roll down along an unknown trajectory, and the effect of the falling stone can be much greater than the impact to which it was subjected. In other words, weak disturbances in his state do not die out, but sharply intensify. True, the stone is sensitive to weak influences only while it is on top of the rock, but there are physical systems that react just as violently to external disturbances over a long period of time. It is precisely such systems that turn out to be chaotic.

So it is with turbulence - small vortex-disturbances that continuously arise in the liquid do not dissolve (as in laminar flow), but constantly increase until the entire movement of water acquires a complex, intricate character. Accordingly, the description of this movement is extremely difficult: a turbulent flow has too many “degrees of freedom”.

As the example of turbulence shows, the behavior of a nonlinear system is difficult to predict - it “responds” to disturbances in its state in a very complex way and, as a rule, ambiguously. Therefore, in order to study nonlinear processes, it is usually necessary to use the so-called “linearization principle,” that is, to reduce a nonlinear system with its inherent ambiguous response to a linear one, which is characterized by completely “reliable” predictable behavior. Essentially, this is a radical simplification and thereby coarsening of the essence of the phenomenon.

But before our eyes, technological progress is accompanied by the emergence of increasingly complex systems, for example, in the energy sector, and how to guarantee the stability of their operation and the complete absence of unpredictable failures is becoming an increasingly important task. Today, new approaches are required, fundamentally A New Look on the problem of analyzing nonlinear processes leading to unpredictable behavior, to “chaos”. And although the essence of order and chaos has not yet been formulated, in last years there was hope to understand the action of unpredictability mechanisms, including transitions “order - chaos” or “chaos - order” (such transitions and their bidirectionality are designated P↔X).

This was facilitated primarily by two factors: firstly, the intensive use of modern computing tools and, secondly, the development of mathematical apparatus, which previously remained only within the confines of “pure theory”. Powerful computers have made it possible to obtain solutions to nonlinear equations in the form of spectacular graphic images - trajectories of the evolution of a dynamic system.

The foundations of a mathematical apparatus suitable for describing “chaos” were laid at the end of the 19th century, but were widely developed only in our time. This was greatly facilitated by the domestic mathematical school of Academician A.N. Kolmogorov, represented by Corresponding Member of the USSR Academy of Sciences V.I. Arnold and Professor Ya.G. Sinai. In the field of applied research, great credit belongs to the schools of Academician A.V. Gaponov-Grekhov and corresponding member of the USSR Academy of Sciences A.S. Monina. Currently, a new, very universal approach to analysis is being formed. nonlinear systems, based on classical results of mathematicians and physicists.

First about the order

Order in a physical, ecological, economic and any other system can be of two types: equilibrium and nonequilibrium. In equilibrium order, when the system is in equilibrium with its environment, the parameters that characterize it are the same as those that characterize the environment; in non-equilibrium order they are different. What is usually meant by such parameters?

In physics, the most important of them is temperature: no equilibrium is possible if the temperature inside the system we are considering is not the same as that of the environment. In this case, heat flows immediately arise, the flow of heat from hot bodies to cold ones begins, which will continue until the temperature is established at the same level for all bodies - both in the system and its environment. Thus, a switched-off electric iron quickly acquires the temperature of the room - the “ambient”: equilibrium is established between it - the system - and the environment. Another important parameter characterizing a physical system is pressure. In equilibrium order, the pressure inside the system must be equal to the pressure on it from the environment. Economic and social systems are also described by generalizing parameters, which at equilibrium take on fixed values.

At first glance, the equilibrium order is more “stable” than the nonequilibrium one. The very nature of the equilibrium order includes resistance to any disturbances in the state of the system (such “stubbornness” in thermodynamics is called Le Chatelier’s principle).

The ability to return to the original state is an indispensable property of the so-called self-regulating systems. And although “self-regulation” is a relatively recent term, it essentially arose along with cybernetics, self-regulating processes are found in nature all the time. Perhaps the most striking example of such a process is a natural nuclear reactor, which operated for approximately half a million years (and, mind you, without stopping for repairs).

In 1972, isotope analysis of ores was carried out at the Oklo uranium deposit in the African Republic of Gabon. It was more of a formality, a “routine”, than something serious. Scientific research. But suddenly, unexpectedly for everyone, the results turned out to be unusual: the concentration of the uranium-235 isotope turned out to be much lower than natural - in some places the depletion (“burnup”) of uranium reached 50 percent. At the same time, researchers discovered a huge excess of such isotopes (neodymium, ruthenium, xenon and others), which usually arise during the fission reaction of uranium-235. The Oklo phenomenon has given rise to many hypotheses, and one of the simplest among them (and therefore the most plausible) leads to a conclusion that is fantastic at first glance: about two billion years ago, a nuclear reactor was launched in Oklo, which operated for about five hundred thousand years. Aliens? Not at all necessary.

To operate the reactor, you need a neutron moderator, such as water. It could accidentally accumulate in deposits with a high concentration of uranium-235 and start a nuclear boiler. And then self-regulation began: with increasing reactor power, a lot of heat was released and the temperature rose. The water evaporated, the neutron moderating layer became thinner, and the reactor power dropped. Then the water accumulated again, and the regulation cycle was repeated.

We rarely think about the fact that the human body exists in a state of non-equilibrium order, when energy losses are compensated by the energy of fuel (food) and oxidizing agent (air). When the life path of an organism ends, it enters a state of complete equilibrium with the environment (equilibrium order).

Physics is a quantitative science, and in order to get a specific result, you need to move from general reasoning to equations and mathematical images. The most useful of these images, with the help of which one can depict the course of a process, the state of a system and the degree of its organization, turned out to be the so-called phase space. The coordinates in this space are various parameters characterizing the system under consideration. In mechanics, for example, these are the positions and velocities of all points whose motion we consider, and therefore in modern analytical mechanics phase space is perhaps the main concept.

Rice. 2

Phase space is, on the one hand, an abstract mathematical space in which the coordinates are the positions and velocities of all points of a physical system, and on the other hand, it is very convenient for a visual description of its evolution. For example, the movement of a ball on a perfectly elastic rubber band, in which there is no friction, is completely determined by the initial speed and position of the ball (initial conditions). Each instantaneous state of such an oscillator - an oscillatory system - corresponds to a point on the phase plane. When the ball oscillates up and down without friction, this point describes a closed curve, and if the oscillations gradually die out, then the phase trajectory converges in a spiral to the limit point corresponding to the stop of the ball. This point is motionless: if the ball is pushed, its phase curve will return to the same point, which, as it were, attracts all nearby trajectories. Therefore, it is called a fixed attracting point, or focus. Such an attractive point - simplest type attractor.

What does the image of processes in phase space give? Here's the thing: only by looking at the “phase portrait” of a physical system can we say whether it is in a state of equilibrium or nonequilibrium order. Moreover, despite their different physical essence, these two types of order can be depicted on the same diagram in the form of clear points, lines and shapes. You can also draw a diagram of the transition from one ordered state to another.

Are geometric images always phase diagram will they be clear? It turns out that there is a class of phenomena that are opposite in order both in physical essence and in the nature of the image on the phase diagram. Their images are blurry, unclear, random, or, as they say, stochastic in nature. Phenomena that give rise to such images are called chaotic.

What is "chaos"?

When New York suddenly plunged into darkness in July 1977, no one even imagined that the cause of the disaster was the transition of the city's energy system from an equilibrium state to a chaotic state, caused by an imbalance in energy production and consumption. Suddenly, a major consumer dropped out of the city's energy system. The automation system and dispatch service did not have time to turn off the generating station equivalent to this consumer, essentially working only for him. A gap emerged between energy generation and consumption, and as a result, the energy system moved from a state of equilibrium to a chaotic one. The “phase portrait” of a system with one frequency (in the USA this frequency is 60 Hz), which is maintained with high accuracy, has turned into a portrait with a huge number of frequencies – “blurred”. The situation continuously worsened, as the system for protecting consumers from random, chaotic voltage surges and frequency failures began to consistently disconnect enterprises from energy sources. It was a real disaster - the collapse of the system. Such disasters are quite rare, but almost every day in large energy systems of the world, phenomena are observed that are not so dangerous, but still cause a lot of trouble. Random, chaotic frequencies “walk” in transmission lines, caused by changes in the operating mode of equipment and imperfect control systems. They cause damage to the economy no less than losses due to resistance in transmission lines - “Joule heat”, which consumes about 20 percent of the world’s electricity.

Typically, chaos has always been understood as disordered, random, unpredictable behavior of system elements. For many years, the dominant theory was that statistical patterns were determined only by the number of degrees of freedom: chaos was believed to be a reflection of the complex behavior of a large number of particles, which, when colliding, create a picture of disordered behavior. The most typical example of such a picture is Brownian motion fine particles in water. It reflects the chaotic thermal movements of a huge number of water molecules randomly striking particles floating in the water, forcing them into random walks. Such a process turns out to be completely unpredictable, non-deterministic, since it is impossible to accurately determine the sequence of changes in the direction of movement of the particle - after all, we do not know how each and every water molecule moves. But what follows from this? But here's what: it becomes impossible to establish such patterns that would make it possible to accurately predict each subsequent change in the trajectory of a particle based on its previous state. In other words, it is not possible to reliably and reliably connect cause and effect or, as experts in mathematical physics put it, to formalize cause-and-effect relationships. This type of chaos can be called nondeterministic (ND). And yet, some average characteristics of behavior in a state of non-deterministic chaos have been found. Using the apparatus of statistical physics, scientists were able to derive formulas that describe some generalized parameters of Brownian motion, for example, the distance traveled by a particle in some time (A. Einstein was the first to solve this problem).

However, in recent years, the attention of researchers has increasingly focused on the so-called deterministic chaos (DC). This type of chaos is generated not by the random behavior of a large number of system elements, but by the internal essence of nonlinear processes. (It was precisely this kind of chaos that led to the energy disaster in New York.) It turns out that deterministic chaos is by no means uncommon: just two elastically colliding billiard balls form a system, the complex behavioral function of which has statistical patterns, that is, it contains elements of “chaos.” Pushing off from each other and from the walls of the billiard table, the balls are scattered at different angles, and through a certain sequence of collisions they can be considered as an unstable dynamic system with unpredictable behavior. Analytical solutions to nonlinear equations describing the behavior of such systems, as a rule, cannot be obtained. Therefore, research is carried out using a computational experiment: on a computer, step by step, numerical values ​​of the coordinates of individual trajectory points are obtained.

In phase space, deterministic chaos is reflected as a continuous trajectory, developing in time without self-intersection (otherwise the process would close into a cycle) and gradually filling a certain region of phase space. Thus, any arbitrarily small zone of phase space intersects infinitely a large number of trajectory segments. This creates a random situation in each zone - chaos: And here’s what’s surprising: despite the determinism of the process - after all, billiard balls are completely subject to classical, “school” mechanics - the course of its trajectory is unpredictable. In other words, we are not able to predict or at least roughly characterize the behavior of the system over a sufficiently large period of time, and primarily because there are fundamentally no analytical solutions.

Order in the frying pan

If you pour a thin layer of some viscous liquid (for example, vegetable oil) into a frying pan and heat the frying pan over a fire, maintaining the temperature of the oil surface constant, then with low heat - low heat flows - the liquid remains calm and motionless. This is a typical picture of a state close to equilibrium order. If you make the fire larger, increasing the heat flow, then after a while - quite unexpectedly - the entire surface of the oil is transformed: it breaks up into regular hexagonal or cylindrical cells. The structure in the pan becomes very similar to a honeycomb. This remarkable transformation is called the Bénard phenomenon, named after the French researcher who was one of the first to study the convective instability of liquids.

Rice. 3

Bénard convective cells. In 1900, an article by the French researcher Benard was published with a photograph of a structure that looked like a honeycomb. When a layer of mercury poured into a flat wide vessel was heated from below, the entire layer unexpectedly disintegrated into identical vertical hexagonal prisms, which were later called Bénard cells. In the central part of each cell, the liquid rises, and near the vertical edges it falls. In other words, directed flows arise in the vessel, which lift the heated liquid (with temperature T1) upward, and lower the cold liquid (with temperature T2) down.

If you continue to increase the heat flow, the cells are destroyed - a transition from order to chaos occurs (P→X). But the most surprising thing is that with even greater heat flows, an alternation of transitions is observed:

X→P→X→P→...!

When analyzing this process, the so-called Rayleigh criterion, proportional to the temperature difference up the oil layer, is selected as a parameter that shows when there will be “order” in the frying pan and when there will be “chaos”, that is, defining the “zone” of order or chaos. This parameter is called the control parameter because it “controls” the transition of the system from one state to another. At critical Rayleigh values ​​(mathematicians call them bifurcation points), “order–chaos” transitions are observed.

Nonlinear equations that describe the formation and destruction of Bénard structures are called Lorentz equations. They connect the phase space coordinates with each other: flow velocities in the layer, temperature and control parameter.

The processes occurring in the vessel can be recorded, for example, by filming and compared with the results of a computational experiment. In Fig. 4 shows just such a comparison. The coincidence of the results of physical and computational experiments is amazing! But before we move on to analyzing these results, we will have to once again turn to phase space.

Rice. 4a

Transitions from order to chaos using the example of the Benard phenomenon. The control parameter, which plays the role of an “adjustment knob,” here is the so-called Rayleigh criterion (Re), proportional to the temperature difference up the liquid layer. “Turning” this control knob corresponds to more or less heating of the liquid. At low heat (Re

Rice. 4b

“Rotating” the adjustment knob further (Re ≈ 10...20), we come to a nonequilibrium order with an attractor like a stable focus - this is in a computational experiment, on a display screen or on a plotter. And in a physical experiment, Benard cells are clearly observed.

Rice. 4v

The dynamics of the process with increasing Rayleigh number is interesting. The distances between the “turns” of the phase trajectory (they are usually called branches) gradually decrease, and eventually the nature of the attractor changes - the focus goes into the limit cycle, which is called the limit cycle because it serves as a boundary curve between the zones of stability and instability; now, even with a very small increase in the control parameter, turbulent vortices begin to form. Order turns into chaos. In a computational experiment, an unstable focus arises, and then a strange attractor appears. In a physical experiment, Benard cells are destroyed, this process resembles boiling.

Why has phase space been such a powerful tool for studying chaos? First of all, because it allows you to present the behavior of a nonlinear, “chaotic” system in a visual way geometric shape. Thus, the behavior of most nonlinear systems in phase space is determined by a certain zone in it, called an attractor (from English to attract). Trajectories depicting the progress of the process are ultimately “attracted” to this zone.

Rice. 5

A strange attractor is an abstract concept introduced to describe a chaotic state. Unfortunately, there is no universal and visual image of a strange attractor. It is possible, however, to construct a children's toy that is a multilayer labyrinth (three-dimensional phase space) along which a ball (representing point) runs. There are holes in the planes between the layers, upon which the ball falls down. However, these holes are not located on the same vertical, and therefore the ball cannot pass through the entire structure. In order for its trajectory to pass from the upper plane to the lower one, the ball must describe bizarre orbits until it hits a hole leading to the neighboring plane. This toy is a rough model of a strange attractor.

As mathematicians have found out, there are two types of attractors: the first is associated with nonequilibrium order and is displayed in phase space by a point (“focus”) or a closed curve (“limit cycle”), the second is associated with the formation of deterministic chaos and is displayed by a limited region of phase space filled a trajectory continuously developing over time (“strange attractor”).

For attractors of the first type, the process trajectories develop as follows. If the system is stable, the trajectory starts from the starting point and ends at either a focus (stable focus) or a limit cycle (stable limit cycle). If the system is unstable, the trajectory begins with either a focus (unstable focus) or a limit cycle (unstable limit cycle) and gradually moves away from its attractor.

If the process is represented by a “strange attractor,” then the trajectory of its evolution begins from the initial point and gradually fills a certain region of phase space. So transitions “order - chaos” in terms of attraction mean a transition from an attractor of the first type (either a focus or a limit cycle) to an attractor of the second type (“strange attractor”).

Now let's return to our frying pan and see how the Benard phenomenon is described in the language of attractors. We have already said that with an increase in heat flow, zones of order and chaos alternate. Here's how it happens.

Everything starts with an equilibrium order. At low heat, when the temperature difference from the frying pan up the layer of liquid is small, there are almost no convective flows in it. And then, regardless of what state the “system” - the liquid in the frying pan - was in at the beginning (as mathematicians say, regardless of the initial conditions), an equilibrium order is maintained in it.

By making the flame under the frying pan a little larger - increasing the heat supply, we will see that the liquid will begin to gradually mix - convection will occur. The lower layers will heat up and become lighter, while the upper layers will remain cold and heavy. The equilibrium of such layers is unstable, and therefore the system passes from an equilibrium order to a nonequilibrium one. Having turned up the heat a little under the frying pan, we will see Benard cells or, as they often say now, simply “Benards” (in the geometric language of phase space, this phenomenon corresponds to an attractor such as a stable focus).

As we continue to heat the liquid in the frying pan, we will soon be able to observe the destruction of the benars. This process resembles boiling - there is a transition from order to chaos (a “strange attractor” has appeared in phase space).

Rice. 6

A well-known example of the use of the chaos-order transition is the laser. However, this example is not the only one. The diagram shows the scientific “zones” known today, in which the transitions “order - chaos” and “chaos - order” are studied and observed, in particular, self-organizing structures (outer circle). In the middle circle there are effects and concepts borrowed by synergetics from related scientific disciplines, and in the inner circle, the various sectors correspond to those new paths and patterns that can be used in each given area of ​​​​knowledge thanks to generalizations made by synergetics.

Today, the search of researchers - mainly mathematicians - is aimed at identifying all types of nonlinear equations, the solution of which leads to deterministic chaos. Active interest in it is caused by the fact that the same patterns can manifest themselves in a variety of natural phenomena and technical processes: with turbulence in flows, instability of electronic and electrical networks, with the interaction of species in living nature, with chemical reactions and even, apparently, in human society. This implies the fundamental significance of chaos - its study can lead to the creation of a powerful mathematical apparatus with great generality and extensive possibilities for applications.

Grigory Fedorovich Muchnik – doctor technical sciences, specialist in the field of energy, State Prize laureate, Honored Worker of Science and Technology of the RSFSR.

Information sources:

1. Prigogine I. From existing to emerging. M., “Science”, 1985.
2. Haken G. Synergetics. Hierarchies of instabilities in self-organizing systems and devices. M., "Mir", 1985.
3. Sinai Ya.G. The randomness of the non-random. M.. “Nature”, No. 3, 1981.
4. Akhromeeva T.S., Kurdyumov S.P., Malinetsky G.G. Paradoxes of the world of non-stationary structures. M., “Knowledge”, 1985.
5. Muchnik G.F. Ordered disorder, controlled instabilities. "Chemistry and Life", No. 5, 1985.
6. How to take advantage of organized clutter. "Chemistry and Life", No. 5, 1986.

Since society is a super complex self-organizing dissipative system, in its history they act - but act in a specific form - general patterns evolution of such systems.

In any dissipative system, two oppositely directed processes occur: one (entropic) leads to the destruction of its structure, disorder and chaos, and the other (anti-entropic) leads to the structuring of the system, an increase in its order. Thus, order arises and exists in conjunction with chaos (both in the external environment and within the system). The relationship between chaos and order is a necessary condition for the existence of dissipative systems.

Self-organization is the result of the synthesis of chaos and order. In a self-organizing system they do not exclude, but, on the contrary, generate and complement each other. Chaos arises from order, and order from chaos. In this case, the birth of order from chaos and chaos from order is determined not by the external environment, but by the internal nature of the dissipative system and the mechanisms operating in it.

The chaos that arises as a result of the destruction of order is “deterministic chaos.” It is caused by those processes that destroy order. It turns out that chaos can be different - depending on how it is formed. Order emerging from chaos also bears the mark of its origin. Chaos, no matter how strange it may seem, is constructive in its very destructiveness: it “burns out” all unnecessary structural formations- unviable, unstable, not integrated into the overall structure of the system. Chaos, therefore, has the ability to give birth to order. He is not an absolute evil, but an important aspect of the processes of self-organization.

“Order is inseparable from chaos. And chaos sometimes appears as super-complex orderliness.”

Order and chaos in a dissipative system constantly accompany each other, but their ratio changes during the evolution of the dissipative system. At some stages order prevails, at others - chaos. Extreme cases are a state of maximum stability, when a stable order reigns in the system, and disorder is reduced to a minimum, and a state of instability, instability, in which chaos quickly increases, and order decreases and can collapse under the influence of the slightest chance. Various modes of system transitions from one state to another are possible.

Considering society as a highly complex dissipative system, social synergetics aims to explore the specifics of its self-organization and the peculiarities of the relationship between social order and social chaos.

A society in which there is no order cannot exist. An unorganized, uncontrollable society in which chaos reigns is doomed to destruction if it does not come out of this state. Living in it is dangerous, and people almost instinctively fear such a life.

T. Hobbes believed that people, realizing the impossibility of living in conditions of complete chaos, when there is a “war of all against all” (omnia bella contra omnes), conclude a “social contract”, according to which they agree to recognize the power of the state over themselves, provided that it will establish law and order in society.

“Lawlessness,” the lack of norms and rules governing people’s behavior, is scary even for hardened criminals; rejecting the authority of the state and the social order established by it, they consider it necessary to have their own “thieves’ law” and their own “authorities.”

But there cannot be a society in which there would be “absolute order” that does not allow any “unauthorized” actions of people. Such a society would become a mechanical system in which individuals and groups would be deprived of all freedom of action. This means that their behavior would become completely algorithmic. In such a society, not only free will, but also reason, in essence, turns out to be redundant, unnecessary and even harmful from the point of view of protecting public order. This mechanical system, strictly speaking, would no longer be a human society. In addition, it would be unable to respond to changes in the external environment and would “break down” either under their influence or due to the “failure” of some of its “cogs”.

Real societies always lie somewhere between these extreme states of “absolute order” and “absolute chaos.” The “historical pendulum” oscillates within the interval separating these states, never reaching it extreme points. But, moving in one direction, it “asymptotically brings” society closer to states of total order, and in the other - to states of monstrous disorder, lawlessness and general chaos. These fluctuations are accompanied by a pulsation of processes of various types: differentiation - integration, hierarchization - dehierarchization, divergence (increasing diversity) - convergence (decreasing it), weakening - strengthening, etc.

It is known from history that there were (and still exist) societies with a harsh despotic regime and severe suppression of all dissent and liberties. Such societies are characterized by the dominance of order over chaos. Societies of this type are called “closed” (A. Bergson, K. Popper), as well as “traditional”, “totalitarian”, “collectivistic” (K. Popper), “mega-tires” (L. Mumford). They are characterized by strict adherence to established traditions, “excessive normativity” of culture, petty regulation of all forms of human life, disapproval of all kinds of creative innovations, hostility to everything foreign, and the desire for self-isolation from neighboring societies. The consequence of all this is their stagnant nature.

Bergson defines a closed society short formula: “authority, hierarchy, immobility.” According to Popper, closed societies are dominated by a magical worldview, taboos, authority and tradition.

Such features were typical of a primitive community, where strict discipline was maintained mainly by the force of tradition and belief. These features were also inherent in ancient states formed in the post-primitive era, with the difference that strict adherence by citizens to the social order established by the state was ensured by the power of totalitarian power, capable of dealing with the disobedient by force. These were the states in Ancient Egypt and China, Ancient Babylon and Assyria, the Inca and Aztec empires, etc.

A social order based on an oppressive totalitarian regime has been the ideal of the “powers that be” throughout history. And they sought to establish it in various forms. In the 20th century it was embodied in fascist states and in states of the Soviet-socialist type. Now he continues to live in countries such as Iraq, Iran, and Taliban Afghanistan.

At the same time, history knows states of society close to complete social chaos. These are “eras of storms and upheavals” associated with mass movements, riots, uprisings, and revolutions. Such conditions are characterized by social unrest, the collapse of political structures, economic ruin, impoverishment, hunger, civil strife, violence and mass bloodshed. Chaos sometimes reaches such a degree that society falls apart and disappears.

The described opposite states of society - the state of “closedness”, in which despotic power dominates, and the state of social chaos - are asymmetrical in relation to time. The first contains a tendency towards stable existence and is capable of persisting over a long historical time. This becomes possible thanks to the formation in society of a hierarchy of fractal structures that repeat the same “pattern” of power at all levels. Fractality makes such a society stable (if it is not fractal, that is, it does not include self-similar structures, then it is unstable and does not exist historically for long - as was the case, for example, with the empire of Alexander the Great). The second state cannot exist for long, because in it the hierarchy is broken social structures and the destruction of fractality. Society strives to get out of this state by restoring social order.

But both of these states are interconnected and give rise to each other. A stagnant totalitarian regime holds back the emerging social changes as long as it is able to do so. Only the fire of social cataclysms can “burn out” its frozen and incapable of improvement social structures. The new is forced to be born in this fire - otherwise it cannot be born in a closed society. But chaos in society is a difficult test for people. It is not for nothing that in China one of the most terrible curses is considered to be: “May you live in an era of change!” The time of change is an intermediate time that ends with the establishment of a new order (even if, as it most often turns out, it is far from what it was seen by the people who started the troubles, and again becomes totalitarian).

In the historical past of mankind, there were many closed societies that existed for more or less a long time, which from time to time exploded with brief outbreaks of social cataclysms and chaos, after which a stable order characteristic of a closed society was re-established.

However, along with this, in the past there were also relatively rare cases of the emergence of more harmonious social systems, in which flexible forms of social order were formed, associated with democracy and allowing relative freedom of thinking and behavior of people. These are, for example, ancient Greek city-states such as Athens or medieval city-republics. The Renaissance era undermines the foundations on which the closed type of society is based. Utopian socialists challenge the state, which guards social inequality and injustice. The Age of Enlightenment (18th century) introduced the ideals of “freedom, equality, fraternity” into public consciousness. In the 19th century V Western Europe harsh regimes of despotic power are increasingly giving way to republican-democratic forms of state. And in the 20th century. The most prosperous countries are those that develop a society built on democratic principles and civil liberties. Such a society, as opposed to a closed one, is called an “open” society.

In an open society, the hierarchy of power structures is placed (to a greater or lesser extent) under the control of the population. The legal system ensures peaceful competition among various political forces in the struggle for power. The election and rotation of government representatives makes power structures more mobile and accessible to renewal. This allows us to improve social order, avoiding destructive social cataclysms and without plunging society into complete chaos. In other words, an open society synthesizes order and chaos, discipline and freedom. And, moreover, in such a way that they seem to mutually prevent the achievement of extreme degrees of both. In society there is a “constantly operating” chaos (freedom), but maintained in certain forms, the local strengthening of which leads to the destruction of individual non-viable social structures while maintaining social order as a whole.

In modern open societies, there are many different voluntary organizations of citizens (communities, foundations, clubs, etc.), which are created by them according to own initiative, and not according to orders from above. The free, unregulated and uncoordinated activity of many such organizations, it would seem, should lead to the disorganization of society. However, in fact, on the contrary, it contributes to the preservation of social order: these organizations are heterogeneous and different in scale fractal structures that harmonize and stabilize society.

An open society is characterized by social mobility, the possibility of moving through levels of the social hierarchy depending on personal achievements and merits, the absence of strict regulation of people’s behavior “from above”, pluralism of opinions, and recognition of the individual’s right to free development. All this stimulates activity, personal initiative and the search for original innovations that can provide more successful solutions to problems of interest to individual social groups and society as a whole. This results in a high rate of its development.

An open society is “a society in which individuals are forced to make decisions.” Expanding opportunities for individual freedom of action increases the chaos of society at the micro level (at the level of individuals) while maintaining the stability of its orderliness at the macro level (at the level of large social structures). Finally, an important feature of an open society is that, in contrast to a closed one, it is open to external contacts and interaction with neighboring societies. If a closed society is “introverted,” then an open society is “extroverted.” Moreover, it cannot develop without exchanging resources with the outside world, without involving other societies in the orbit of its interests and in the process of solving its problems.

This explains the fact that the emergence and development of open societies is accompanied by active - and often aggressive - economic, political and cultural expansion into other countries. The history of the British Empire is a vivid example of such expansion. The experience of history shows that closed societies cannot withstand the onslaught of open ones. Their resistance to this onslaught continues, but perhaps the 20th century. was the last century in which major closed world powers emerged and lasted for several decades - Nazi Germany and Soviet Union. It can be noted that after their fall, Western-style civilization began to more intelligently implement the principles of an open society, and public opinion in Western countries began to more resolutely defend the need for peaceful development. Along with the spread of the economic, political and cultural influence of open societies, the desire to assimilate the experience accumulated in other societies has intensified.

The creation of open societies necessarily generates a trend towards globalization historical development humanity. In the second half of the 20th century. this trend led to general cultural exchange, the formation of a global economic market, and the emergence of a single political field for interaction between all states of the Earth.

In the light of what has been said, it is obvious that the development of an open society is not just a fact of the internal history of an individual people, but a turning point in the history of all mankind.

“The transition from a closed society to an open one can be described as one of the most profound revolutions that humanity has gone through.”

Of course, closed and open societies are not separated from each other by a Chinese wall. History knows many intermediate options that carry the features of both types of society. We are talking only about a long historical era, during which, through various intermediate forms, the transformation of open society into the main type of social systems occurs.

With the establishment and spread of open societies, the “amplitude” of oscillations of the “historical pendulum” decreases. Humanity shows a desire - and finds means of its implementation - not to bring these fluctuations to the extreme states of a closed society and social chaos.

However, the “pendulum-like” course of historical processes continues, leading to a cyclical alternation of periods of a relatively stable, ordered state and “times of change,” disturbance, and instability. These “waves of history” in an open society become less stormy, but it “sways” in them, experiencing alternating periods of evolution and periods of crisis in some particular sphere of social life or society as a whole. During periods of evolution, a regime of more or less smooth, orderly, “laminar” flow of events is established, and during periods of crisis, a “turbulent,” unstable, more or less chaotic flow of unpredictable changes arises.

Truth is random, selective and constantly changing, but it changes in such a way that the whole world, to which it relates 100%, also changes, which is why I perceive Chaos as the mental basis, the substance of the world, of everything that exists, but not material, but ideological. On the basis of this constantly changing substance of the world, I can make decisions, cognize and create, that is, make movement and progress, therefore it is Chaos, and not disorder. This is the quintessence of Chaos as primary, and not some fantasies like Chaos as the first matter or substrate, these are all errors introduced by the categories of materialism that has dominated science and philosophy for a long time.

Therefore, you, the reader, need to reconsider what you may have thought when reading the disadvantages of chaos at the beginning of the book and what you are absorbing now. Since this is the movement of truth, its slippage, its progress; its mobility and changeability, its relationship to the world as primacy, the determinants of foundations, “monads of monads” is one of the reasons for its elusiveness by a too slow mind; but part of this truth can be realized and understood, since the mind at a specific stage of its development catches up with the elusive stage that the truth has already passed in its movement, the very stage where the mind is able to understand it, but since the truth has already changed, the mind is left with only mental atavism from the object he was chasing and again he continues his research, his movement. This is a kind of pursuit, but at such stages the mind can use parts of the acquired ghost of truth, the one that is not truth, but was, and on the basis of this, explore the mechanism. But this same mechanism is constantly in motion, and all these probabilities, all these changing mechanisms are Chaos, and attempts to understand all this is the knowledge of Chaos. And what I said about chaos has not changed, but chaos as the cult of chaos is only a cult, but not as a non-occult tradition of knowledge of Chaos with a reverent attitude towards it due to the awareness of the consequences of errors in the study of this kind of phenomena and noumena.

So, Chaos (Greek - beginning, revelation) is a term that appeared in ancient Greek cosmogony meaning the primary state of a megasystem, for example the universe. It is characterized by the absence of any form of embodiment, that is, understanding it abstractly, it is a resource, a basis, a potential that requires and is capable of being built according to one or another model, acquiring a form - a substrate. Substrate (Latin substratum - foundation) is the basis of all things in its processes.

Chaos only later began to be identified with disorder, but neither the authors of the concept itself, nor chaosists, nor those who study chaos in occultism share such a confusion of concepts, since it is not true. Christianity itself brought together the concepts of chaos and disorder in view of the fact that chaos denoted that real thing that was imputed by Christianity to their god Jehovah, Sabaoth, and so on in the history of creation, while the authors of the concept, the ancient Greeks, understood chaos as the abyss containing all the potentialities of existence. . Disorder is, first of all, the lack of potential for creativity, creation; it is a mass that always changes its state, which is what differs from chaos, which has a basic unchangeable sign of something, for example, substance as a product of chaos.

Chaos as in cosmogony ancient Greece harmoniously fit into the universe, and now in any science or philosophy it is harmoniously woven into the cosmogony of the latter. So, for example, the theory of the “Big Bang” is nothing more than a theory about the production of the substance of the material world by chaos, which resulted in the self-organized formation of order, that is, the world with the consequences of the process of origin, namely the laws that reality built for itself based on that type of structure into which it was organized out of chaos. The latter illustrates the potential of chaos for order, which disorder is incapable of (without intervention). The difference between chaos in this case and order is that chaos carries within itself the ability for many types of order, speaking more broadly, as well as understanding these phenomena and noumenon more broadly, we can say that chaos carries within itself many orders in so many organizations that any the order-disorder relationship, just as there is a complete possibility of chaos returning to its original (original, more correctly, present) state - the state of Chaos. All other states of movement of chaos are transitional stages of the existence of the order-disorder relationship, because in no system, even an insignificantly small one - a microsystem, there is an achieved order in existence; a share of disorder is present everywhere, one of its forms, for example, entropy. That is, chaos in its present state is a resource that contains truth and is limited only by it. So, for example, the appearance of reason among human individuals is a product of the potential for orderliness; reason itself brings effective ordering, including understanding and knowledge. The random movement of oxygen molecules in a room cannot lead to a state of vacuum in part of the room, since it is associated with the order that a uniform distribution of air in the room has been established. This is how disorder and order are connected, one gives rise to the other, limits it, but also allows it to exist. Yes, there is a possibility that all the air will be in one part of the room, and in another part there will be a vacuum, this could happen if there was only one disorder, but this is not the case. The connection between order itself and the disorderly is not the essence of chaos, it is a consequence in a given world and with its present type of structure into which it was organized. With another change, the movement of chaos from its present state, everything may turn out to be different, but the all-relative and all-applicable quantity, relating to any state, noumenon and phenomenon - truth - will not change. That is, truth is a mechanism, structural magnitude and freedom of chaos in the perception of a given discourse.

At different structures and degrees of deployment and integration of the world there can exist different types chaos, which leads to the following consequences, which are too early to think about in principle, since the truth that stands at the forefront is nothing more than the subject of knowledge of chaos itself. Occultism in general and Satanism in particular, exploring chaos, collects information about this very truth, why it is and how it can be used is said at the beginning of this paragraph, and I will talk about occultism in particular and the cult in Satanism in the second volume of this book.

Thus, the cult of the substratum of the world is nonsense, as is the cult of an object or thing, like the cult of pantheism, for example. Philosophy that studies chaos is also no different from the branch of occultism that studies the same thing, and so on. Thus, chaos can only be defined as a concept in occultism about chaos as a substrate and more in the cosmogony of modern research thought. Yes, we will have to be content with abstractions, something better, something worse, than objective data for as long as objective knowledge of the subject itself will be impossible, that is, never under the conditions of the present level of intelligence of researchers. Only abstract and subjective (in defense of the subjective itself is said in this book) knowledge and models are capable of giving an idea or understanding of the world to the mind, which is not surprising, since what else is subjective used if the mind itself is largely subjective.

Regardless of the category of knowledge that considers objects and objects of Chaos, order and ordered, be it cosmogony, ontology or anything else, these objects and objects are important determinants of existence. Chaos as potency and source of movement (development, improvement) of existence; ordered as an actual, conditional equilibrium of the system ensured by the mutual balance of disorder and order; as well as order as a completed movement, the achieved deployment of a system, the achievement of the limit of development, at which all movements are eliminated due to the exhaustion of their resources and potential. Because of the latter, we can talk about the cult of Chaos among intelligent beings, since the alternative order contains neither interest for the mind, nor even the possibility of the existence of this very mind.

Simply put, order is a picture of the world captured in the final, completed moment. The world or worlds - the existing one - will achieve order when it has completely completed its organization and exhausted the potential and resources for movement - development and improvement. Yes, order, to some extent, is the natural completion of any development, but not improvement. And the mind is a constant movement, regardless of whether this movement is performed by a particle or an idea, this is already a problem of perception and interpretation of movement depending on the direction of science and philosophy. So, when order is a complete and static state of any system and, moreover, of all their diversity, then this is death, or rather the disappearance, exclusion of the mind due to the fact that the mind is basically a constant movement - perception, thinking, imagination, reason it is a generator, a producer of ideas from the resources of both the external environment and from one’s internal resources - something, that is, the mind is a miniature Chaos (after all, I am a microcosm), and a certain mind is a certain semblance of Chaos. For these two reasons, firstly, order is the exclusion of reason, and secondly, reason is miniature Chaos, there is a cult of Chaos. In my opinion, there are completely rational grounds, in contrast to the hackneyed socio-psychological model, that this order is obviously better. It's up to you, reader, to decide for yourself.

Genres: Fantastic

Annotation:

A little about creation. Draft version.

Posted by: 25/04/2016

Changed: 25/04/2016

Chaos, order and reason.

Could a war aimed at the complete destruction of the enemy be a way out of the accumulated and tangled tangle of contradictions for the intelligent? Is it possible to reconcile civilizations colliding in a narrow field, with different methods of development, so radically different from each other? Whether anyone else in the universe will be able to repeat the path of the Sower race and whether they have chosen the right path in their development will be shown by the upcoming grandiose clash of several fundamentally different civilizations that have achieved their power. Meanwhile, Selariel is intensively preparing for terrible war, which the Commonwealth still doesn’t even know about.

This was an epoch-making event for the earth. In response to an external request, a long-distance communication module, long forgotten as unnecessary, was activated. Manager Iskin himself did not know why, after so many years of fruitless attempts to get in touch with at least someone, he did not rework this block into something more useful and relevant. Rationalism failed, the instructions spoke of the need for such a module, while the real need for it had long since disappeared, as unnecessary. Distributed consciousness, obeying useless and outdated directives, continued the fruitless ineffective control and support in an active state of long-distance communication systems.

This was the first connection request in 50 million years or more. After receiving and sending the automatic codes prescribed by the connection protocol, Iskin model SGY3245GHR45 seriously thought about whether he should answer this call in full access and communication mode. A new feeling came, something he had never experienced before, a feeling of fear. The long period of complete loneliness was over; now Iskin could not answer the main question to himself: is he happy about this event?

If at the very beginning, thrown into an unexplored area of ​​the galaxy, torn apart by a cosmic catastrophe, he, according to all the instructions laid down in him, desperately called on his creators on all available communication channels, since the situation was clearly out of control and was beyond his competence. At first, he was ready to do anything if only those who were used to making decisions would appear. Iskin was ready to give them the fullest access, if only they would solve the problem that arose before him. The signal went nowhere, no one responded.

The Reptilians, as a defense at the distant borders around their system, created an area of ​​anomalous space that interfered with free movement, which led to the disaster. The colonizer of the sower race was thrown out of hyperspace near the planet itself; the emergency exit from the jump occurred at too high a speed. The colonizer ship, controlled by artificial intelligence, did everything possible until the last moment; its main goal was to minimize the consequences of the disaster and save the colonists.

Over the next few tens of millions of years, Iskin desperately struggled with the unruly planet that had survived global catastrophe, developing terraforming algorithms from scratch again, without having sufficient knowledge and tools for this. He was ready to fulfill any wish of anyone who would tell him how to do everything right. No one, despite desperate calls, came to the aid of the colonialist who had suffered a catastrophe; he had to search and find solutions on his own. He searched, fought and did not give up, somewhere reinventing, somewhere using the few grains of information that remained intact.

Everything collapsed, nothing came of the intense work that lasted for tens of millions of years, the system continued to remain unstable, in need of constant correction, and the colony, instead of developing, lost the knowledge that it had. Only after the “lost colony” mission finally collapsed, and the colonists who survived the planetary cataclysm were deeply degraded, did Iskin remove his supervision from the survivors. By some strange coincidence, at that moment he felt a feeling far from relieved. Melancholy and hopelessness came, the meaning of life and his existence was lost.

This is probably similar to how someone fell in love with the sea, studied a lot of drawings, built a yacht with their own hands, spending a lot of money and time on it, and it sank as soon as it was launched. The old woman was left with nothing, but she had such grandiose plans.

After all, it’s not even funny to serve those who worship the pyramids, primitive creatures who have embarked on the path of self-destruction. The descendants of the sowers have rolled back too much in development, even if recently they have stirred more actively, several times awakening Iskin from a state of deep melancholy with underground nuclear explosions. The savages even began to explore nearby outer space using primitive chemical rockets, without ever revealing the secret of gravity. An extremely absurd civilization was built by the descendants of the colonists, who along the path of progress in their development collected all the mistakes that they could. Autonomous probes sent to investigate these strange creatures into which the once great conquerors of the universe had turned attracted unnecessary attention, giving rise to a chain of rumors about UFOs and similar heresies. Iskin, immersed hundreds of kilometers into the planet’s crust, had to temporarily curtail the active phase of observation.

The path by which this civilization developed went nowhere, people polluted the entire planet, fought among themselves for crumbs of resources and, most importantly, had no development potential. At one time, Iskin seriously worked on the idea of ​​clearing the surface of the degraded descendants of their owners, they began to pollute too much environment, but something prevented him from bringing this thought to fruition. Perhaps he remembered that the race of sowers had only three creatures, called the destroyer, who had the right to determine who would live. Each case of the destruction of a dead-end civilization was carefully examined from all sides. Only in case of complete inability to develop, and not at all due to different views or morals, could the sowers clear entire galaxies of weeds, leaving room for the development of useful civilizations.

Bristling their weapons against each other, the earthlings did not even notice that for seven years now alien guests had been regularly landing on the planet, kidnapping and exporting thousands of their compatriots as living goods. Iskin first became interested in those who arrived from distant stars, maybe they are worthy of more complete contact and are capable of taking control. The results of the research were depressing, there was also complete disorder. The aliens had the crudest primitive technologies for piercing space, distorted genetics with many accumulated system errors leading to early death, and nothing that would interest a super intelligence.